Sub-band coding refers to a technique where, by the parallel application of a set of analysis filters, an input signal is decomposed into several sub-band signals that are separately coded for the purpose of transmission. For reconstruction after transmission, the individual sub-band signals are decoded and filtered using a set of synthesis filters in order to reproduce the original signal. Sub-band coding was first developed in connection with the coding and transmission of speech signals. (See e.g., R. E. Cochiere et al, "Digital Coding of Speech in Sub-bands BSTJ", Vol. 55, pp. 1069-1085).
For the sub-band coding and transmission of a video signal, separable analysis filter banks are applied first horizontally then vertically to each field of a video signal. Application of a filter bank, comprising two filters, first horizontally then vertically, gives rise to an analysis of a video signal into four frequency sub-band signals: horizontal-low, vertical-low; horizontal-low, vertical-high; horizontal-high, vertical-low; horizontal-high, vertical-high. Each resulting sub-band signal is encoded according to its own statistics for transmission from a transmitting station to a receiving station. At the receiving station the individual sub-band signals are decoded and the original signal is reconstructed using vertical and horizontal synthesis filter banks.
A very important part of the design of a sub-band coding system is the choice of the analysis and synthesis filter banks that are used to decompose and reconstruct the original video signal.
A requirement imposed on the filter banks is that in the absence of coding and quantization distortion, the filter banks should provide a substantially exact reconstruction of the sub-band coded signal. In view of the large amount of data that needs to be processed for the decomposition and reconstruction of video signals such as HDTV signals, a further requirement for the sub-band coding of a video signal is that the signal processing algorithms carried out by the analysis and synthesis filters be simple enough to allow low cost real time implementation. However, the two above-mentioned requirements--i.e., the requirement for exact reconstruction of sub-band coded signals and the requirement for the filters to carry out simple signal processing algorithms--severely limits the choice of filters.
Up to now, the sub-band coding of video signals has been carried out primarily using finite impulse response (FIR) filter banks. However, such FIR filter banks are generally quite complex, especially for the real-time decomposition and reconstruction of video signals. See e.g., J. W. Woods et al., "Sub-band Coding of Images", IEEE Trans. on Acoust., Speech, Signal Processing, Vol. ASSP-34 No. 5 pp. 1278-1288, October '86; M. Vetterli "Multi-Dimensioned Sub-band Coding: Some Theory and Algorithms", Signal Processing Vol. 6 pp. 97-112 April 1988; P. H. Westerink et al., "Sub-band Coding of Images Using Predicture Vector Quantization." IEEE International Conf. on Acoust., Speech, Signal Processing, ICASS 87, pp. 1378-1381, Dallas, April 1987.
In addition to the requirements mentioned above, for the sub-band coding of video signals, it is desirable to use filters whose responses exhibit phase linearity. Phase linearity allows the creation of a hierarchical signal representation wherein the sub-band signal carrying the low frequency information can be displayed without significant distortion. For example, when an HDTV signal is sub-band coded, the horizontal-low, vertical-low sub-band signal can be utilized by itself by a non-HDTV receiver. A set of especially simple linear phase FIR filters for the sub-band coding of video signals is disclosed in D. J. LeGall et al, "Sub-band Coding of Digital Images Using Short Kernel Filters and Arithmetic Coding Techniques", PROC IEEE Int. Conf. on Acoust., Speech, Signal Processing, April 1988.
As an alternative to FIR filters, infinite impulse response (IIR) filters may be considered. (See R. Ansari et al., "Two dimensional IIR Filters for Exact Reconstruction in Tree-Structured Sub-band Decomposition", Electronic Letters, Vol. 23, pp. 633-634, June 1987 and T. T. Ramstad, "IIR Filter Bank for Sub-band Coding of Images", ISCAS '88 pp 827-830). The use of IIR filters is motivated by the fact that IIR filters often produce sharper filter cut-offs with lower filter orders. Previous attempts (see e.g. the Ramstad reference, supra) to apply IIR filters to the sub-band decomposition and reconstruction of video images have resulted in IIR filters whose implementation is too complex to be practical in real HDTV systems. In particular, such conventional IIR filters, when utilized in connection with the sub-band decomposition and reconstruction of HDTV signals, require extremely high processing speeds and the synthesis filter banks would require memory capacity for a full field of video.
Accordingly, it is an object of the present invention to provide filters for use in connection with the sub-band decomposition and reconstruction of video images which are simple to implement. In particular, it is an object of the present invention to provide approximately linear phase filters with simple coefficients which enable an original signal to be analyzed and synthesized with minimal computational complexity and which enable substantially exact reconstruction of the original signal.